With just three speeds, there's of course a compromise between the overall spread and the gear step size. The overall spread/gear step size of today's basic SRAM, Shimano and Sturmey-Archer three speeds is very nearly the same and represents the compromise that was settled on around one hundred years ago. Here's a suggestion from New Departure back in the early 1950s about how to set up a three speed:
This looks useful but it is too small to read; do you have a link to a site with this info? Thank you.